2019/05/24 by Du Rong, Du, Rong, Xinyi Fang +3
Mathematics · Medicine · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Phytoestrogen effects and research
paper · pdf · doi:10.48550/arxiv.1905.10151
openalex publication_date 2019/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study vector bundles on flag varieties over an algebraically closed field k. In the first part, we suppose G=Gk(d,n) (2≤ d≤ n-d) to be the Grassmannian manifold parameterizing linear subspaces of dimension d in kn, where k is an algebraically closed field of characteristic p>0. Let E be a uniform vector bundle over G of rank r≤ d. We show that E is either a direct sum of line bundles or a twist of a pull back of the universal bundle Hd or its dual Hd\vee by a series of absolute Frobenius maps. In the second part, splitting properties of vector bundles on general flag varieties F(d1,⋯,ds) in characteristic zero are considered. We prove a structure theorem for bundles over flag varieties which are uniform with respect to the i-th component of the manifold of lines in F(d1,⋯,ds). Furthermore, we generalize the Grauert-Mulich-Barth theorem to flag varieties. As a corollary, we show that any strongly uniform i-semistable (1≤ i≤ n-1) bundle over the complete flag variety splits as a direct sum of special line bundles.